- Open Access
- Article
Product in Product Type Estimator with Exponential and Log Function to Estimate Population Mean Using DSS
by Sangeeta Malik 
, Rubal Sharma and Ruchi Gupta
Baba Mastnath University Asthal Bohar Rohtak,Haryana, Department of Mathematics, 124021, India
* Author to whom correspondence should be addressed.
Journal of Engineering Research and Sciences, Volume 4, Issue 2, Page # 11-17, 2025; DOI: 10.55708/js0402002
Keywords: Finite population mean, Bias, Mean Squared Error, Double sampling for stratification (DSS
Received: 14 January 2025, Revised: 05 February 2025, Accepted: 06 February 2025, Published Online: 11 February 2025
(This article belongs to the Special Issue Special Issue on Multidisciplinary Sciences and Advanced Technology 2024 & Section Biochemical Research Methods (BRM))
APA Style
Sharma, R., Malik, S., & Gupta, R. (2025). Product in product type estimator with exponential and log function to estimate population mean using DSS. Journal of Engineering Research and Sciences, 4(2), 11–17. https://doi.org/10.55708/js0402002
Chicago/Turabian Style
Sharma, Rubal, Sangeeta Malik, and Ruchi Gupta. “Product in Product Type Estimator with Exponential and Log Function to Estimate Population Mean Using DSS.” Journal of Engineering Research and Sciences 4, no. 2 (2025): 11–17. https://doi.org/10.55708/js0402002.
IEEE Style
R. Sharma, S. Malik, and R. Gupta, “Product in Product Type Estimator with Exponential and Log Function to Estimate Population Mean Using DSS,” Journal of Engineering Research and Sciences, vol. 4, no. 2, pp. 11–17, 2025, doi: 10.55708/js0402002.
To estimate the population, mean in two-phase stratified sampling, this paper aims to construct a new product in the product type estimator using exponential and log functions. When using two samples for stratification, this study attempts to solve the equation for bias and mean squared error (MSE) up to the first degree of approximation (fda). The modified estimator is more effective than y‾ds (the usual unbiased estimator,Y‾ˆ PPds(Ige & Tripathi ratio estimator) and YˆPPe (ratio type exponential estimator) given by Tailor et al. theoretically and numerically. Finding out how the proposed estimators stack up against the state-of-the-art is the main motivation for this research. Extensive evaluation of the estimator’s performance in a simulated environment. The suggested estimators perform better than other estimators, according to both theoretical and practical studies.
- I. Aslam, M. Noor-Ul Amin, M. Hanif, and P. Sharma, “Memory type ratio and product estimators under ranked-based sampling schemes,” Communications in Statistics – Theory and Methods, vol. 52, 1155–1177, 2023, doi: 10.1080/03610926.2021.1924784.
- S. Bahl and R. K. Tuteja, “Ratio and product type exponential estimators,” Journal of Information and Optimization Sciences, vol. 12, no. 1, 159–164, 1991, doi: 10.1080/02522667.1991.10699058.
- W. G. Cochran, “The estimation of the yield in cereal experiments by sampling for the ratio of grain to total produce,” The Journal of Agricultural Science, vol. 30, 262–275, 1940, doi: 10.1017/S0021859600048012.
- M. Dalabehara and L. N. Sahoo, “A new estimator with two auxiliary variables for stratified random sampling,” Statistica, vol. 59, no. 1, 101–107, 1999, doi: 10.6092/issn.1973-2201/1106.
- A. Gupta and R. Tailor, “Ratio in ratio type exponential strategy for the estimation of population mean,” Journal of Reliability and Statistical Studies, vol. 14, no. 2, 551–564, 2021, doi: 10.13052/jrss0974-8024.1429.
- A. F. Ige and T. P. Tripathi, “On double sampling for stratification and use of auxiliary information,” Journal of the Indian Society of Agricultural Statistics, vol. 39, no. 2, 191–201, 1987.
- C. Kadilar and H. Cingi, “Ratio estimators in stratified random sampling,” Biometrical Journal, vol. 45, no. 2, 218–225, 2003.
- B. Kiregyera, “Regression type estimators using two auxiliary variables and the model of double sampling,” Metrika, vol. 31, 215–226, 1984, doi: 10.1007/BF01915203.
- N. Koyuncu and C. Kadilar, “Ratio and product estimators in stratified random sampling,” Journal of Statistical Planning and Inference, vol. 139, no. 9, 2552–2558, 2009, doi: 10.1016/j.jspi.2009.02.005.
- P. Mehta and R. Tailor, “Chain ratio type estimators using known parameters of auxiliary variates in double sampling,” Journal of Reliability and Statistical Studies, vol. 13, no. 2–4, 243–252, 2020, doi: 10.13052/jrss0974-8024.13242.
- M. N. Murthy, Sampling Theory and Methods, Calcutta, India: Statistical Publishing Society, 1967, vol. xxiv, 684. [Online]. Available:
https://www.cabidigitallibrary.org/doi/full/10.5555/19702700466 - M. K. Pandey, G. N. Singh, T. Zaman, A. Mutairi, and M. Mustafa, “A general class of improved population variance estimators under non-sampling errors using calibrated weights in stratified sampling,” Scientific Reports, vol. 14, 2948, 2024, doi: 10.1038/s41598-023-47234-1.
- M. Rueda, S. Martínez, H. Martínez, and A. Arcos, “Estimation of the distribution function with calibration methods,” Journal of Statistical Planning and Inference, vol. 137, no. 2, 435–448, 2007, doi: 10.1016/j.jspi.2006.02.002.
- J. Shabbir and S. Gupta, “Improved ratio estimators in stratified sampling,” American Journal of Mathematical and Management Sciences, vol. 25, no. 1–2, 293–311, 2005, doi: 10.1080/01966324.2005.10737666.
- H. P. Singh and P. Nigam, “Ratio-Ratio-Type exponential estimator of finite population mean in double sampling for stratification,” International Journal of Agricultural and Statistical Science, vol. 16, no. 1, 251–257, 2020a. [Online]. Available: https://www.researchgate.net/profile/Pragati-Nigam/publication/345161967_RATIO-RATIO-TYPE_EXPONENTIAL_ESTIMATOR_OF_FINITE_POPULATION_MEAN_IN_DOUBLE_SAMPLING_FOR_STRATIFICATION/links/5faad4cfa6fdcc331b930530/RATIO-RATIO-TYPE-EXPONENTIAL_ESTIMATOR_OF_FINITE_POPULATION_MEAN_IN_DOUBLE_SAMPLING_FOR_STRATIFICATION.pdf
- H. P. Singh and P. Nigam, “Product-Product-Type exponential estimator of finite population mean in double sampling for stratification,” International Journal of Mathematics and Statistics, vol. 20, no. 1, 165–179, 2022. [Online]. Available: https://www.researchgate.net/profile/Pragati-Nigam/publication/360699467_A_General_Class_of_Product-cum-Ratio-Type_Exponential_Estimators_in_Double_Sampling_for_Stratification_of_Finite_Population_Mean/links/6285e53e247e622c2efb57d7/A-General-Class-of-Product-cum-Ratio-Type-Exponential-Estimators-in-Double-Sampling-for-Stratification-of-Finite-Population-Mean.pdf
- M. Yaqub and J. Shabbir, “Estimation of population distribution function in the presence of non-response,” Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 2, 471–511, 2018. [Online]. Available: https://dergipark.org.tr/en/pub/hujms/issue/38251/442321
- T. Zaman and C. Kadilar, “Exponential ratio and product type estimators of the mean in stratified two-phase sampling,” AIMS Mathematics, vol. 6, no. 5, pp. 4265–4279, 2021. [Online]. Available: https://pdfs.semanticscholar.org/a208/bfac5a1185c7e0a368f1e004e12f5d24d714.pdf
